# How do you solve using gaussian elimination or gauss-jordan elimination, x+y+z=3, 2x+2y-z=3, x+y-z=1 ?

Jan 18, 2016

This set of equations has no solution

#### Explanation:

Initial Augmented Matrix:
[ ( 1.00, 1.00, 1.00, 3.00), ( 2.00, 2.00, -1.00, 3.00), ( 1.00, 1.00, -1.00, 1.00) ]

Pivot Action $n$
pivot row = n; pivot column = n; pivot entry augmented matrix entry at (n,n)

$$1. convert pivot n row so pivot entry = 1
2. adjust non-pivot rows so entries in pivot column = 0


Pivot $\textcolor{b l a c k}{1}$
Pivot Row 1 reduced by dividing all entries by 1.00 so pivot entry = 1
[ ( 1.00, 1.00, 1.00, 3.00), ( 2.00, 2.00, -1.00, 3.00), ( 1.00, 1.00, -1.00, 1.00) ]

$$Non-pivot rows reduced for pivot column
by subtracting appropriate multiple of pivot row 1 from each non-pivot row


[ ( 1.00, 1.00, 1.00, 3.00), ( 0.00, 0.00, -3.00, -3.00), ( 0.00, 0.00, -2.00, -2.00) ]

Pivot $\textcolor{b l a c k}{2}$
Pivot row 2 has a 0-valued pivot entry; exchange attempted
No subsequent rows have a non-zero value in the pivot column

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Given equations allow for no solution
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